ALBERT

Description: The Earth’s iron-rich inner core is seismically anisotropic, which may be due to the preferred orientation of Fe-rich hexagonal close packed (hcp) alloy crystals. Elastic anisotropy in a hexagonal crystal is related to its c / a axial ratio; therefore, it is important to know how this ratio depends on volume (or pressure), temperature, and composition. Experimental data on the axial ratio of iron and alloys in the Fe–Ni–Si system from 15 previous studies are combined here to parameterize the effects of these variables. The axial ratio increases with increasing volume, temperature, silicon content, and nickel content. When an hcp phase coexists with another structure, sample recovery and chemical analysis from each pressure-temperature point is one method for determining the phase’s composition and thus the position of the phase boundary. An alternate method is demonstrated here, using this parameterization to calculate the composition of an hcp phase whose volume, temperature, and axial ratio are measured. The hcp to hcp+B2 phase boundary in the Fe–FeSi system is parameterized as a function of pressure, temperature, and composition, showing that a silicon-rich inner core may be an hcp+B2 mixture. These findings could help explain observations of a layered seismic anisotropy structure in the Earth’s inner core.

Description: Synchrotron X-ray diffraction data were obtained to simultaneously measure unit-cell volumes of W and WO 2 at pressures and temperatures up to 70 GPa and 2300 K. Both W and WO 2 unit-cell volume data were fit to Mie-Grüneisen equations of state; parameters for W are K T = 307 (±0.4) GPa, K ' T = 4.05 (±0.04), 0 = 1.61 (±0.03), and q = 1.54 (±0.13). Three phases were observed in WO 2 with structures in the P 2 1 / c , Pnma , and C 2/ c space groups. The transition pressures are 4 and 32 GPa for the P 2 1 / c-Pnma and Pnma-C 2/ c phase changes, respectively. The P 2 1 / c and Pnma phases have previously been described, whereas the C 2/ c phase is newly described here. Equations of state were fitted for these phases over their respective pressure ranges yielding the parameters K T = 238 (±7), 230 (±5), 304 (±3) GPa, K ' T = 4 (fixed), 4 (fixed), 4 (fixed) GPa, 0 = 1.45 (±0.18), 1.22 (±0.07), 1.21 (±0.12), and q = 1 (fixed), 2.90 (±1.5), 1 (fixed) for the P 2 1 / c , Pnma , and C 2/ c phases, respectively. The W-WO 2 buffer (WWO) was extended to high pressure using these W and WO 2 equations of state. The T - f O 2 slope of the WWO buffer along isobars is positive from 1000 to 2500 K with increasing pressure up to at least 60 GPa. The WWO buffer is at a higher f O 2 than the iron-wüstite (IW) buffer at pressures lower than 40 GPa, and the magnitude of this difference decreases at higher pressures. This implies an increasingly lithophile character for W at higher pressures. The WWO buffer was quantitatively applied to W metal-silicate partitioning by using the WWO-IW buffer difference in combination with literature data on W metal-silicate partitioning to model the exchange coefficient ( K D ) for the Fe-W exchange reaction. This approach captures the non-linear pressure dependence of W metal-silicate partitioning using the WWO-IW buffer difference. Calculation of K D along a peridotite liquidus predicts a decrease in W siderophility at higher pressures that supports the qualitative behavior predicted by the WWO-IW buffer difference, and agrees with findings of others. Comparing the competing effects of temperature and pressure the results here indicate that pressure exerts a greater effect on W metal-silicate partitioning.

Description: A mineral intermediate between sillimanite and mullite, tentatively designated as "sillimullite," was studied by electron microprobe analyses and single-crystal X-ray diffraction methods. The chemical compositions derived from the microprobe results and the crystal-structure refinement are Al 7.84 Fe 0.18 Ti 0.03 Mg 0.03 Si 3.92 O 19.96 and Al 8.28 Fe 0.20 Si 3.52 O 19.76 (Fe is Fe 3+ ) corresponding to x -values of 0.02 and 0.12, respectively, in the solid-solution series Al 8+4x Si 4–4x O 20–2x assigning Fe 3+ , Ti, and Mg to the Al site. The composition derived from microprobe analysis is very close to a stoichiometric sillimanite (with Fe 3+ ,Ti, and Mg assigned to Al sites), while the composition derived from diffraction data is midway between sillimanite and Si-rich mullites. The discrepancy is assumed to be caused by the occurrence of amorphous nano-sized SiO 2 inclusions in the aluminosilicate phase not affecting the diffraction data but detected in the microprobe analysis. "Sillimullite" crystallizes in the orthorhombic space group Pnam with a = 7.5127(4), b = 7.6823(4), c = 5.785(3) Å, V = 333.88(4) Å 3 , Z = 1. It has a complete Si/Al ordering at tetrahedral sites like sillimanite but with neighboring double chains of SiO 4 and AlO 4 tetrahedra being offset by 1/2 unit cell parallel to c relative to each other causing the change of the space-group setting from Pbnm (sillimanite) to Pnam . Difference Fourier calculations and refinements with anisotropic displacement parameters revealed the formation of oxygen vacancies and triclusters as known in the crystal structures of mullite. Final refinements converged at R 1 = 5.9% for 1024 unique reflections with F o 〉 4( F o ). Fe was found to reside predominantly in the octahedral site and with minor amounts in one of the T* sites. Mg and Ti were not considered in the refinements. The crystal studied here is considered to represent a new mineral intermediate between sillimanite and mullite, named "sillimullite."

Description: The high-cosmic abundance of sulfur is not reflected in the terrestrial crust, implying it is either sequestered in the Earth’s interior or was volatilized during accretion. As it has widely been suggested that sulfur could be one of the contributing light elements leading to the density deficit of Earth’s core, a robust thermal equation of state of iron sulfide is useful for understanding the evolution and properties of Earth’s interior. We performed X-ray diffraction measurements on FeS 2 achieving pressures from 15 to 80 GPa and temperatures up to 2400 K using laser-heated diamond-anvil cells. No phase transitions were observed in the pyrite structure over the pressure and temperature ranges investigated. Combining our new P-V-T data with previously published room-temperature compression and thermochemical data, we fit a Debye temperature of 624(14) K and determined a Mie-Grüneisen equation of state for pyrite having bulk modulus K T = 141.2(18) GPa, pressure derivative K ' T = 5.56(24), Grüneisen parameter 0 = 1.41, anharmonic coefficient A 2 = 2.53(27) x 10 –3 J/(K 2 ·mol), and q = 2.06(27). These findings are compared to previously published equation of state parameters for pyrite from static compression, shock compression, and ab initio studies. This revised equation of state for pyrite is consistent with an outer core density deficit satisfied by 11.4(10) wt% sulfur, yet matching the bulk sound speed of PREM requires an outer core composition of 4.8(19) wt% S. This discrepancy suggests that sulfur alone cannot satisfy both seismological constraints simultaneously and cannot be the only light element within Earth’s core, and so the sulfur content needed to satisfy density constraints using our FeS 2 equation of state should be considered an upper bound for sulfur in the Earth’s core.

Description: This is a comprehensive compilation of refractive indices of 1933 minerals and 1019 synthetic compounds including exact chemical compositions and references taken from 30 compilations and many mineral and synthetic oxide descriptions. It represents a subset of about 4000 entries used by Shannon and Fischer (2016) to determine the polarizabilities of 270 cations and anions after removing 425 minerals and compounds containing the lone-pair ions (Tl + , Sn 2+ , Pb 2+ , As 3+ , Sb 3+ , Bi 3+ , S 4+ , Se 4+ , Te 4+ , Cl 5+ , Br 5+ , I 5+ ) and uranyl ions, U 6+ . The table lists the empirical composition of the mineral or synthetic compound, the ideal composition of the mineral, the mineral name or synthetic compound, the Dana classes and subclasses extended to include beryllates, aluminates, gallates, germanates, niobates, tantalates, molybdates, tungstates, etc., descriptive notes, e.g., structure polytypes and other information that helps define a particular mineral sample, and the locality of a mineral when known. Finally, we list n x , n y , n z , 〈 n Dobs 〉 (all determined at 589.3 nm), 〈 n Dcalc 〉, deviation of observed and calculated mean refractive indices, molar volume V m , corresponding to the volume of one formula unit, anion molar volume V an , calculated from V m divided by the number of anions (O 2– , F – , Cl – , OH – ) and H 2 O in the formula unit, the total polarizability 〈α AE 〉, and finally the reference to the refractive indices for all 2946 entries. The total polarizability of a mineral, 〈α AE 〉, is a useful property that reflects its composition, crystal structure, and chemistry and was calculated using the Anderson-Eggleton relationship \[ {{\upalpha }}_{\hbox{ AE }}=\frac{\left({n}_{\hbox{ D }}^{2}-1\right){V}_{\hbox{ m }}}{4{\uppi }+\left(\frac{4{\uppi }}{3}-c\right)\left({n}_{\hbox{ D }}^{2}-1\right)} \] where c = 2.26 is the electron overlap factor. The empirical polarizabilities and therefore, the combination of refractive indices, compositions, and molar volumes of the minerals and synthetic oxides in the table were verified by a comparison of observed and calculated total polarizabilities, 〈α AE 〉 derived from individual polarizabilities of cations and anions. The deviation between observed and calculated refractive indices is 〈2% in most instances.

Description: An extensive set of refractive indices determined at = 589.3 nm ( n D ) from ~2600 measurements on 1200 minerals, 675 synthetic compounds, ~200 F-containing compounds, 65 Cl-containing compounds, 500 non-hydrogen-bonded hydroxyl-containing compounds, and ~175 moderately strong hydrogen-bonded hydroxyl-containing compounds and 35 minerals with very strong H-bonded hydroxides was used to obtain mean total polarizabilities. These data, using the Anderson-Eggleton relationship \[ {{\upalpha }}_{T}=\frac{\left({n}_{D}^{2}-1\right){V}_{m}}{4{\uppi }+\left(\frac{4{\uppi }}{3}-c\right)\left({n}_{D}^{2}-1\right)} \] where α T = the total polarizability of a mineral or compound, n D = the refractive index at = 589.3 nm, V m = molar volume in Å 3 , and c = 2.26, in conjunction with the polarizability additivity rule and a least-squares procedure, were used to obtain 270 electronic polarizabilities for 76 cations in various coordinations, H 2 O, 5 H x O y species [(H 3 O) + , (H 5 O 2 ) + , (H 3 O 2 ) – , (H 4 O 4 ) 4– , (H 7 O 4 ) – ], $${\mathrm{NH}}_{4}^{+}$$ , and 4 anions (F – , Cl – , OH – , O 2– ). Anion polarizabilities are a function of anion volume, V an , according to $${{\upalpha }}_{-}={{\upalpha }}_{-}^{0}\cdot {10}^{-{N}_{\mathrm{o}}/{V}_{\hbox{ an }}^{1.20}}$$ where α – = anion polarizability, $${{\upalpha }}_{-}^{\mathrm{o}}=\hbox{ free-ion polarizability }$$ , and V an = anion molar volume. Cation polarizabilities depend on cation coordination according to a light-scattering (LS) model with the polarizability given by $${{\upalpha }}_{(CN)}={\left({a}_{1}+{a}_{2}CN{e}^{-{a}_{3}CN}\right)}^{-1}$$ where CN = number of nearest neighbor ions (cation-anion interactions), and a 1 , a 2 , and a 3 are refinable parameters. This expression allowed fitting polarizability values for Li + , Na + , K + , Rb + , Cs + , Mg 2+ , Ca 2+ , Sr 2+ , Ba 2+ , Mn 2+ , Fe 2+ , Y 3+ , (Lu 3+ -La 3+ ), Zr 4+ , and Th 4+ . Compounds with: (1) structures containing lone-pair and uranyl ions; (2) sterically strained (SS) structures [e.g., Na 4.4 Ca 3.8 Si 6 O 18 (combeite), = 6% and Ca 3 Mg 2 Si 2 O 8 (merwinite), = 4%]; (3) corner-shared octahedral (CSO) network and chain structures such as perovskites, tungsten bronzes, and titanite-related structures [e.g., MTiO 3 (M = Ca, Sr, Ba), = 9–12% and KNbO 3 , = 10%]; (4) edge-shared Fe 3+ and Mn 3+ structures (ESO) such as goethite (FeOOH, = 6%); and (5) compounds exhibiting fast-ion conductivity, showed systematic deviations between observed and calculated polarizabilities and thus were excluded from the regression analysis. The refinement for ~2600 polarizability values using 76 cation polarizabilities with values for Li + -〉 Cs + , Ag + , Be 2+ -〉 Ba 2+ , Mn 2+/3+ , Fe 2+/3+ , Co 2+ , Cu +/2+ , Zn 2+ , B 3+ -〉 In 3+ , Fe 3+ , Cr 3+ , Sc 3+ , Y 3+ , Lu 3+ -〉 La 3+ , C 4+ -〉 Sn 4+ , Ti 3+/4+ , Zr 4+ , Hf 4+ , Th 4+ , V 5+ , Mo 6+ , and W 6+ in varying CN’s, yields a standard deviation of the least-squares fit of 0.27 (corresponding to an R 2 value of 0.9997) and no discrepancies between observed and calculated polarizabilities, 〉 3%. Using \[ {n}_{\mathrm{D}}=\sqrt{\frac{4{\uppi }{\upalpha }}{\left(2.26-\frac{4{\uppi }}{3}\right){\upalpha }+{V}_{m}}+1} \] the mean refractive index can be calculated from the chemical composition and the polarizabilities of ions determined here. The calculated mean values of 〈 n D 〉 for 54 common minerals and 650 minerals and synthetic compounds differ by 〈2% from the observed values. In a comparison of polarizability analysis with 68 Gladstone-Dale compatibility index (CI) ( Mandarino 1979 , 1981 ) values rated as fair or poor, we find agreement in 32 instances. However, the remaining 36 examples show polarizability values 〈3%. Thus, polarizability analysis may be a more reliable measure of the compatibility of a mineral’s refractive index, composition, and crystal structure.